Estimation of stress-strength reliability in s-out-of-k system for new flexible exponential distribution under progressive type-II censoring

Abstract

This article addresses stress-strength reliability estimation in s-out-of-k systems under progressive type-II censoring.  The system consists of components facing common stress, where stress and strength variable follows independent new flexible exponential (NFE) distributions, sharing a common parameter. The estimation procedure is carried out using MLE, Bayesian estimation and uniformly minimum variance unbiased estimation (UMVUE) techniques. MLE is derived for known and unknown common parameters. Bayesian estimates are obtained using Lindley’s approximation and Markov chain Monte Carlo techniques due to the complexity of obtaining the exact Bayesian estimates, when the common parameter is unknown. Moreover, UMVUE is derived when the common parameter is known. The 95% asymptotic confidence interval, highest posterior density credible intervals, and Bayesian credible intervals, are constructed. An extensive simulation study is carried out to compare the performance of various censoring schemes and estimation methods. Finally, two progressively censored real datasets are analyzed for illustration.

Keywords:

• Reliability
• new flexible exponential distribution
• progressive type-II censoring
• maximum likelihood estimation
• Bayesian estimation
• simulation

Acknowledgements

The authors extend their heartfelt appreciation to the editors and esteemed reviewers for their invaluable and constructive feedback, which has significantly contributed to the enhancement of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to acknowledge the financial support by Kerala State Council For Science, Technology and Environment (KSCSTE). [Grant number: KSCSTE/972/2018-FSHP-MAIN].